Combining Loan Rates by Matching Total EMI Cash Flows

Summary

The document asks how to combine two loans with different principal amounts and interest rates when both have the same repayment term. A weighted average of the annual rates produces a monthly installment slightly below the sum of the installments calculated for each loan separately. The answer treats the combined borrowing as a single annuity: add the principals, add the monthly payments, and use the common number of payments to solve for the rate that discounts those payments to the combined principal.

For the stated example, the resulting annualized IRR is 10.42543%, which reproduces the combined installment amount. This works because the two component annuities have equal term and payment frequency, so their summed cash flows form an annuity with the same schedule. The result is an implied rate for those combined cash flows; the document does not establish a general weighted-rate rule for loans with different terms or repayment timing.

Key ideas

• The sum of equal-term annuities is an annuity with principal and payment amounts equal to the respective sums.
• To find the combined rate, solve the annuity rate from the total principal, payment, and number of periods.
• A principal-weighted average of nominal rates may not reproduce the combined installment cash flow.
• The method relies on matching payment schedules and terms across the component loans.

Tags

# Calculation of Combined IRR


# Calculation of Combined IRR












How to calculate combined IRR for two different cost of funds? The emi (Equated Monthly Installment) amount, whether it is calculated separately or based on the combined IRR should be same. I tried using weighted average for combining the IRRs but difference is arising in EMI amount.

Cost 1 $600000

Interest - 8% P.A

Cost 2 $400000

Interest - 14% P.A

Period - 24 months

EMI 1 $27136.37

EMI 2 $19205.15

Total - $46341.53

I calculated weighted average by (600000*8%+400000*14%)/(600000+400000)

Weighted IRR is 10.40%

EMI based on weighted IRR is 46329.76

Difference of 11.76.

Please provide a formula for calculation of combined IRR for (1000000) which should provide the same EMI amount of 46341.53.

## Answer by Alex C (score 1)

https://quant.stackexchange.com/a/45620

The sum of 2 annuities of the same length is still an annuity.

You have a monthly annuity with PV = 600000+400000 = 1000000

Number of payments N = 24

Amount of monthly payment PMT = 27136.37+19205.15 = 46341.53

Then using the RATE(N,-PMT,PV)*12 function in Excel or similar Annuity function in a financial calculator you find the IRR to be 10.42543%

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.